44. A biconvex lens has a radius of curvature of magnitude 20 cm. Which one of the following options best describe the image formed of an object of height 2 cm placed 30 cm from the lens?

44. A biconvex lens has a radius of curvature of magnitude 20 cm. Which one of the following options best describe the image formed of an object of height 2 cm placed 30 cm from the lens ?

(a) Virtual, upright, height = 1 cm

(b) Virtual, upright, height = 0.5 cm

(c) Real, inverted, height = 4 cm

(d) Real, inverted, height = 1 cm

Answer :  (c) Real, inverted, height = 4 cm

\( R = 20 \ \text{cm} \)

\( \frac{1}{f} = ( n_{21} - 1 ) \cdot \frac{2}{R} \)

 

\( = ( 1.5 - 1 ) \cdot \frac{2}{20} \)

\( = \frac{1}{2} \cdot \frac{2}{20} \)

\( = 20 \ \text{cm} \)

\( u = -30 \ \text{cm} \) 

(negative because the object is on the left of the lens in sign convention)

\( \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \)

\( \frac{1}{20} = \frac{1}{v} - \frac{1}{-30} \)

\( \frac{1}{20} = \frac{1}{v} + \frac{1}{30} \)

\( \frac{1}{v} = \frac{1}{20} - \frac{1}{30} \)

\( \frac{1}{v} = \frac{3 - 2}{60} = \frac{1}{60} \)

\( v = 60 \ \text{cm} \)

\( h_o = 2 \ \text{cm} \)

\( m = \frac{v}{u} = \frac{60}{-30} = -2 \)

\( h_i = m \cdot h_o = -2 \times 2 = -4 \ \text{cm} \)

( The negative sign means inverted. )